are.pargld.valid {lmomco} | R Documentation

## Are the Distribution Parameters Consistent with the Generalized Lambda Distribution

### Description

The distribution parameter object returned by functions of this package such as by `vec2par` are consistent with the corresponding distribution, otherwise a list would not have been returned. However, other functions (`quagld`) require consistent parameters to ensure that the Generalized Lambda Distribution is monotonic increasing on 0 <= F <= 1, in which F is nonexceedance probability.

### Usage

    are.pargld.valid(para,verbose=FALSE,nowarn=FALSE)

### Arguments

`para` | A distribution parameter list returned by `vec2par`.
`verbose` | A logical switch on additional output to the user—default is `FALSE`.
`nowarn` | A logical switch on warning surpression. If `TRUE` then `options(warn=-1)` is made and restored on return. This switch is to permit calls in which warnings are not desired as the user knows how to handle the returned value—say in an optimization algorithm.

### Details

Karian and Dudewicz (2000) outline valid parameter space of the Generalized Lambda distribution. First, according to Theorem 1.3.3 the distribution is valid if and only if

α(kappa F^{kappa - 1} + h(1-F)^{h -1 }) >= 0 mbox{.}

for all F in [0,1]. The `are.pargld.valid` function tests against this condition by incrementing through [0,1] by dF = 0.0001. This is a brute force method of course. Further, Karian and Dudewicz (2002) provide a diagrammatic representation of regions in kappa and h space for suitable α in which the distribution is valid. The `are.pargld.valid` function subsequently checks against the 6 valid regions as a secondary check on Theorem 1.3.3. The regions of the distribution are defined for suitably choosen α by

mbox{Region 1: } kappa <= -1 mbox{ and } h >= 1 mbox{,}

mbox{Region 2: } kappa >= 1 mbox{ and } h <= -1 mbox{,}

mbox{Region 3: } kappa >= 0 mbox{ and } h >= 0 mbox{,}

mbox{Region 4: } kappa <= 0 mbox{ and } h <= 0 mbox{,}

mbox{Region 5: } h >= (-1/kappa) mbox{ and } -1 >= kappa <= 0 mbox{, and}

mbox{Region 6: } h <= (-1/kappa) mbox{ and } h >= -1 mbox{ and } kappa >= 1 mbox{.}

### Value

`TRUE` | If the parameters are `gld` consistent.
`FALSE` | If the parameters are not `gld` consistent.

### Note

This function calls `is.gld` to verify consistency between the distribution parameter object and the intent of the user.

### Author(s)

W.H. Asquith

### References

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions—The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

### See Also

`is.gld`

### Examples

    para <- vec2par(c(123,34,4,3),type='gld')
    if(are.pargld.valid(para)) Q <- quagld(0.5,para)

[Package lmomco version 0.92 Index]